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• Aexp

Aexp-count

Measure for recurring over aexp structures.

Signature

(aexp-count x) → count

Arguments

x — Guard (aexpp x).

Returns

count — Type (natp count).

Definitions and Theorems

Function: aexp-count

(defun aexp-count (x)
  (declare (xargs :guard (aexpp x)))
  (let ((__function__ 'aexp-count))
    (declare (ignorable __function__))
    (case (aexp-kind x)
      (:const 1)
      (:var 1)
      (:add (+ 3 (aexp-count (aexp-add->left x))
               (aexp-count (aexp-add->right x))))
      (:mul (+ 3 (aexp-count (aexp-mul->left x))
               (aexp-count (aexp-mul->right x)))))))

Theorem: natp-of-aexp-count

(defthm natp-of-aexp-count
  (b* ((count (aexp-count x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: aexp-count-of-aexp-fix-x

(defthm aexp-count-of-aexp-fix-x
  (equal (aexp-count (aexp-fix x))
         (aexp-count x)))

Theorem: aexp-count-aexp-equiv-congruence-on-x

(defthm aexp-count-aexp-equiv-congruence-on-x
  (implies (aexp-equiv x x-equiv)
           (equal (aexp-count x)
                  (aexp-count x-equiv)))
  :rule-classes :congruence)

Theorem: aexp-count-of-aexp-add

(defthm aexp-count-of-aexp-add
  (implies t
           (< (+ (aexp-count left) (aexp-count right))
              (aexp-count (aexp-add left right))))
  :rule-classes :linear)

Theorem: aexp-count-of-aexp-add->left

(defthm aexp-count-of-aexp-add->left
  (implies (equal (aexp-kind x) :add)
           (< (aexp-count (aexp-add->left x))
              (aexp-count x)))
  :rule-classes :linear)

Theorem: aexp-count-of-aexp-add->right

(defthm aexp-count-of-aexp-add->right
  (implies (equal (aexp-kind x) :add)
           (< (aexp-count (aexp-add->right x))
              (aexp-count x)))
  :rule-classes :linear)

Theorem: aexp-count-of-aexp-mul

(defthm aexp-count-of-aexp-mul
  (implies t
           (< (+ (aexp-count left) (aexp-count right))
              (aexp-count (aexp-mul left right))))
  :rule-classes :linear)

Theorem: aexp-count-of-aexp-mul->left

(defthm aexp-count-of-aexp-mul->left
  (implies (equal (aexp-kind x) :mul)
           (< (aexp-count (aexp-mul->left x))
              (aexp-count x)))
  :rule-classes :linear)

Theorem: aexp-count-of-aexp-mul->right

(defthm aexp-count-of-aexp-mul->right
  (implies (equal (aexp-kind x) :mul)
           (< (aexp-count (aexp-mul->right x))
              (aexp-count x)))
  :rule-classes :linear)